Dual-state systolic architecture for recursive least-squares updating and downdating

Orthogonal updating/hyperbolic downdating has been used for sliding window RLS estimation. While orthogonal updating is numerically stable, hyperbolic downdating can be unstable under certain ill-conditioned cases. We propose a new downdating scheme based on the reversed operations of the updating method utilizing orthogonal transformations. An example modeling some highly non-stationary data illustrates the advantage of the proposed scheme. This proposed downdating scheme can still be implemented on a previously known efficient dual-state systolic architecture for performing sliding window RLS estimation.